Question: Solve for $x$ and $y$ using elimination. $\begin{align*}4x-y &= -6 \\ -4x-5y &= -3\end{align*}$
Solution: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-6y = -9$ Divide both sides by $-6$ and reduce as necessary. $y = \dfrac{3}{2}$ Substitute $\dfrac{3}{2}$ for $y$ in the top equation. $4x- \dfrac{3}{2} = -6$ $4x-\dfrac{3}{2} = -6$ $4x = -\dfrac{9}{2}$ $x = -\dfrac{9}{8}$ The solution is $\enspace x = -\dfrac{9}{8}, \enspace y = \dfrac{3}{2}$.